The VISA network (VisaNet) supports 4.4 Trillion dollars of commerce per year (2009). If we assume (somewhat arbitrarily), that the Bitcoin Days Destroyed metric approaches 50% (half of all coins are used every day, on average, to facilitate transactions),
then the value of the Bitcoin required to support 10% of the transactional volume in the VISA network (once all coins are minted) is $4.4T * 10% = $440B / 365 days/year / (21M BTC * 50%) = $114.80.

Does this approach seem valid? 50% BTCDD is arbitrary. 10% of the VISA network, is arbitrary but seems like a reasonable goal. What needs to be changed to improve this estimate, and what would a better way if any to compute the imputed value of the BTC based on its use as a transactional currency, rather than a speculative store of value?

I do not get the assumptions that it could be doing 10% of the volume of visa, but that no one would be holding all their coins for more then a day.
– osmosisSep 20 '11 at 18:55

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@osmosis The 10% assumption is somewhat arbitrary, but is used to size the opportunity for Bitcoin relative to the largest payment process network that exists today (VISA). If you accept that assumption, then the next question is: how many of the total number of Bitcoins will be utilized daily to facilitate the assumed velocity? If the answer is only 10%, then the imputed value of the BTC actually needs to be 5x higher, or $574. Likewise, if we assume that the Bitcoin only ever supports 1% of the VISA network with just 5% of the coins in transition per day, the implied value is smaller.
– Andrew JonesSep 20 '11 at 20:28

2 Answers
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"Bitcoin days destroyed" seems like a bogus metric. Transactions in the block chain do not always represent an actual economic trade. Wallets routinely resign the remainder of a coin to a new private key and it's very hard to determine what is the transaction and what is the change. You could spend 0.5 BTC from a 50 BTC block mined 10 days ago, and resign 49.5 BTC to yourself - you have "destroyed" 500 bitcoin days as far as the metric is concerned.

You don't have to care about the proportion of currency circulating, just the average velocity. Us dollar M1 velocity is in the 8 - 10 range. That means that on average a dollar changes hands every 1-1.5 months. If we assume a similar dynamic for say 10 million bitcoins (2 years from now?), we get about $4400/BTC for 10% of your quoted Visa volume.

But 10% of that is very, very much. It includes 1500bln in cash/ATM and 1700bln in credit purchases. The online commerce part of that than Bitcoin could target is maybe 200bln dollars and 10% of that brings the price of one bitcoin to 200$.

And all this assuming the deflation does not choke the velocity - which it will, bringing the actual volume down and with it the incentive for businesses to invest in bitcoin support.

Assuming your M1 comparison is accurate and holds at 'full' adoption as a transitional currency, this may indeed be a valid way to think about the problem. Assuming the BTC supports $20B of commerce annually at a velocity of 10x, the value of the BTC once fully issued (21M BTC total) is ~$100.
– Andrew JonesSep 27 '11 at 18:45

The M1 velocity of 8 is for a quarter, not an entire year. See the "What is bitcoin velocity" section. And you forgot to divide by the velocity. $4.4 trillion × 0.1 ÷ (4 × 8 x 10 million) = $1375. If online market is only $200bln and Bitcoin takes 10% with velocity of 8 per quarter, then the Quantity Theory of Money value of bitcoin is $62.5.
– Shelby Moore IIIMar 23 '13 at 15:36

As I explained in another answer, we can not meaningfully use measures of dormancy from P2P currencies in Quantity Theory of Money comparisons relative to GDP (or in Visa's case total Q over the period).

I also explained in that linked answer why it is unlikely that Bitcoin would obtain the same velocity multiple of 8 per quarter as with fiat.

Expounding, in order to get that many round-trips per quarter, requires the network effects of a wide diversity of available goods and services which only comes with economies-of-scale. So it is a chicken-and-egg dilemma.

Based on that, the true quarterly velocity of Bitcoin may be on the order of a intuitive guess of 1, so with 10% of the a $200bln online economy (as proposed by the prior answer), with 21 millions coins, I calculate:

$200bln × 0.1 ÷ (4 × 1 x 21 million) = $238

A lower velocity means a higher FX price for Bitcoins, but a low velocity also probably means low adoption for transacting, thus I am skeptical of the 10% assumption.

One could make a wild guess and claim either 1% share with 1 velocity or 10% share with 10 velocity thus:

$200bln × 0.01 ÷ (4 × 1 x 21 million) = $23.8

$200bln × 0.1 ÷ (4 × 10 x 21 million) = $23.8

Note we are dividing by M × V (inverted the Quantity Theory of Money equation), because we want the exchange price in dollars, not the price of goods and services in bitcoin.

It should be noted the Quantity Theory of Money is probably not the main factor that will drive the Bitcoin's exchange price, because Bitcoin is predominantly a speculation system and subject to volatility manipulation. So (irrational) confidence will likely drive the value of Bitcoin (as is often the case with illiquid small cap “investments” or pseudo-pyramid schemes). In a speculative frenzy, the marketcap of Bitcoin could rise well above any realistic estimate of its Quantity Theory of Money value.